Constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds. (English) Zbl 1208.83023
Summary: We follow the approach employed by Y. Choquet-Bruhat, J. Isenberg and D. Pollack [Classical Quantum Gravity 24, No. 4, 809–828 (2007; Zbl 1111.83002)] in the case of closed manifolds and establish existence and non-existence results for constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds.
MSC:
83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
83C40 | Gravitational energy and conservation laws; groups of motions |